For a letter to the editor of the Daily Breeze (a newspaper in Torrance,
Ca) from Richard Wagoner about the final outcome of the LAUSD Algebra I
Pacing Plan, along with an earlier letter and reply from District K administrator
Howard M. Vogel, click here.

An Open Letter to the LAUSD School Board and Superintendent
Romer

September 25, 2002

Dear Superintendent Romer and LAUSD Board Members;

We are writing to draw your attention to the potentially negative impact
of the Los Angeles Unified School District Pacing Plan for Algebra I students.
It is our opinion, as LAUSD high school math teachers, scientists, and
university mathematicians, that the LAUSD Pacing Plan for Algebra I should
be dropped.

The LAUSD Pacing Plan for Algebra I prescribes the order in which topics,
sections, and chapters of Algebra I textbooks are to be presented to LAUSD
students, in the 8th and 9th grades. LAUSD has two individualized
pacing plans for each of the three textbooks for Algebra I used in LAUSD.
One of the pacing plans for each textbook is designed for the two year
Algebra I course based on that book, and the other pacing plan is for a
one year course based on that textbook. Both plans cover approximately
the same topics in algebra.

One of the textbooks used for Algebra I in LAUSD is "Algebra I: Structure
and Method" by Brown, Dolciani, et al. This textbook has been approved
by the California State Board of Education. In contrast to the most widely
used Algebra I textbook in LAUSD, "Concepts and Skills," the textbook "Algebra
I: Structure and Method" received a positive review from mathematicians
appointed by the State Board of Education to evaluate the Algebra I textbooks
for statewide adoption. The official Content Review Panel Report
for all three Algebra I textbooks used in LAUSD, written by four university
mathematics professors, is available at:

According to the summary of the Content Review Panel Report for "Algebra
I: Structure and Method":

"We recommend this book highly. The book is well-organized,
and topics are clearly and precisely explained. We found no inaccuracies,
terminological or otherwise. Where possible, facts are proved/explained,
not just asserted or concluded from a few examples. There are many problems,
including word problems, of a range of difficulty."

A copy of the LAUSD pacing plan for "Algebra I: Structure and Method"
is included at the end of this letter. It undermines the organization
of ideas in this textbook, and it undermines the California Mathematics
Framework and Standards. We illustrate with some examples.

The two year pacing plan for "Structure and Method" calls for the quadratic
formula together with completing the square of quadratic polynomials (in
Chapter 12 of the textbook) to be explained to students before basic factoring
techniques for polynomials (in Chapter 5), and before an introduction to
radicals, including techniques for simplifying radicals (in Chapter 11).
This choice of ordering of topics is so mathematically unsound that it
will most likely seriously undermine the ability of LAUSD math teachers
to teach algebra in a coherent and meaningful way. It will reduce the learning
of algebra to memorizing meaningless formulas without understanding.
In the words of the chairman of the Math Department of San Pedro High School
(in LAUSD), Richard Wagoner:

"First and foremost among the problems with the Pacing Plan
is that
it renders the textbook and all support materials useless and obsolete.
The sequence is so seemingly random that students must jump back and
forth between sections of chapters through most of the course.
Therefore, all review materials, diagnostic tests, supplementary
materials and enriched materials -- all of which are tied to the
sequence as designed by the authors -- can no longer be used."

Unfortunately, this pacing plan is being forced on high school math
teachers in District K of LAUSD, according to Richard Wagoner.

Here is another example of ordering of topics by the two-year algebra
plan:

Solving Systems of Linear Equations, in Chapter 9, is to be presented
in the third quarter of the first year. The material in Chapter 9
requires that students have a clear understanding of Section 7-3, "Equations
With Fractional Coefficients." But Section 7.3 is postponed by the
pacing plan until the fourth quarter of the first year. Chapter 9 also
relies on prerequisites in Chapter 4 that are not presented until
the first quarter of the second year. For example, the addition method
of solving systems of linear equations requires an understanding of adding
and subtracting polynomials, a topic in Chapter 4 presented long after
it is needed.

The examples described here are not exhaustive, and the one-year Algebra
course topics are also poorly ordered. Among the serious defects
of the pacing plan for the one-year course is the complete omission of
Chapter 11. Students are thus expected to use the quadratic formula without
a complete understanding of square roots, and practice in simplifying radicals.

The apparent purpose of the Pacing Plan is to organize topics within
the Algebra I curriculum so that each topic is taught at nearly the same
time in all Algebra I classes at LAUSD schools (for the one year and two
year courses, respectively), regardless of which textbook is used. Not
only does the Pacing Plan seriously undermine the mathematical content
of Algebra I by scrambling topics without regard to logical order and prerequisites,
it even fails to meet the modest goal of ordering topics so that they are
taught at the same time, independent of the textbook. A comparison
of the Pacing Plans for "Concepts and Skills," "Structure and Method,"
and "Prentice Hall Algebra I" shows that the plans are not coordinated
with each other. Richard Wagoner reports the following inconsistencies
for the one-year algebra class plans:

a) The topic of functions is introduced in the second quarter of the
year for "Structure and Method" and for "Concepts and Skills,"
but only in the fourth quarter for the Prentice Hall book.

b) Solving Inequalities is presented in the second quarter for "Structure
and Method" and in the first quarter for the other two books.

c) Rate-Time-Distance problems are introduced in the third quarter for
"Structure and Method," the second quarter for the Prentice Hall text,
and not all in "Concepts and Skills."

d) Square roots are not in the pacing plan for "Structure and Method"
but they are presented in the third quarter for "Concepts and Skills,"
and the fourth quarter for the Prentice Hall text.

e) Quadratic polynomials are studied in the third quarter for "Structure
and Method" and "Concepts and Skills", but in the fourth quarter
for Prentice Hall.

f) Percents are explained in the fourth quarter for "Structure and Methods"
but in the first quarter for the other two texts.

The LAUSD Pacing Plan thus does not comport with the California Math
Framework. According to the Framework (page 231):

"The order of presentation of mathematical topics is mathematically
and pedagogically sound."

"Prerequisite skills and ideas are presented before the more complex
topics that depend on them."

"Student materials ensure that students can look back in the textbook
for help with understanding a topic; compilations, such as indices, tables
of contents, and review summaries, also provide assistance."

The textbook, "Structure and Method" was adopted and approved for use
in California schools because it is well aligned to the Framework.
The effect of the Pacing Plan is to compromise and weaken this alignment
to the California Framework and Standards.

It is our opinion that well written textbooks play an important role
in mathematics education generally, and the teaching of algebra specifically.
The view that a "standards driven math program" should not be "text driven"
and therefore that "jumping around" shouldn't cause too much distress is
misguided. Algebra teachers should be encouraged to take advantage
of the logical development of algebra available in the best state standards
aligned textbooks, as well as review problems in these books, and other
teaching tools. We urge you to drop the Pacing Plan and allow LAUSD
algebra teachers to teach the subject coherently and in a logical order.

Sincerely,

Richard Wagoner, Chair
Department of Mathematics
San Pedro High School (LAUSD)

David Klein
Professor of Mathematics
California State University, Northridge

Nenita Andres-Sandor
Department of Mathematics
San Pedro High School

Robert Baker
Assistant Principal
San Pedro High School

Jessica Barker
Department of Mathematics
San Pedro High School (LAUSD)